def _F2(a, b, c):
if b == c:
return 6 * _H(a, c)
return (a + b + c)**2 / (3 * (b - c)**2) * (
(b + c) / (math.sqrt(b * c)) * float(mpm.elliprf(a / b, a / c, 1)) +
(2 * a - b - c) /
(3 * math.sqrt(b * c)) * float(mpm.elliprd(a / b, a / c, 1)) - 2)
def _F1(a, b, c):
if a == b:
return 3 * _H(c, a)
if a == c:
return 3 * _H(b, a)
return (a + b + c)**2 / (18 * (a - b) * (a - c)) * (
math.sqrt(b * c) / a * float(mpm.elliprf(a / b, a / c, 1)) +
(3 * a**2 - a * b - a * c - b * c) /
(3 * a * math.sqrt(b * c)) * float(mpm.elliprd(a / b, a / c, 1)) - 1)
def bi(ai):
# ->> t: time list <<- #
#b=np.zeros(3)
idxall = np.arange(3)
b = []
for i in range(3):
idx = np.delete(idxall, i)
#print 'calculating RD at', idx[0], idx[1], i
#b.append(2./3.*(mpmath.elliprd(ai[idx[0]], ai[idx[1]], ai[i])*np.prod(ai)-1.))
b.append(
np.float64(
2. / 3. *
mpmath.elliprd(ai[idx[0]]**2., ai[idx[1]]**2., ai[i]**2.) *
np.prod(ai)))
return b
def get_Ax(*, x, y, z):
"""
Returns the degenerate Carlson symmetric elliptic integral of the third kind. Note that the permutation of the first
two arguments does not change the result
"""
return float(2 / 3 * (elliprd(y**2, z**2, x**2)))